Degenerate parametric curves
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Cited by (19)
Conics in rational cubic Bézier form made simple
2024, Computer Aided Geometric DesignThe uniqueness of the rational Bézier polygon is unique
2022, Computer Aided Geometric DesignCitation Excerpt :Thus, the situation differs from that of the polynomial case, where procedure (i) restricts to a linear transformation, and (iii) is unavailable. Procedures (ii), (iii), which do change the degree and hence the control polygon, yield a degenerate representation (Sederberg, 1984). By ruling them out, considering only non-degenerate representations (i.e., properly parameterized and of irreducible degree), we characterize the uniqueness of the control polygon:
Algebraic and geometric characterizations of a class of planar quartic curves with rational offsets
2020, Computer Aided Geometric DesignComment on the "coincidence condition of two Bézier curves of an arbitrary degree"
2015, Computers and Graphics (Pergamon)Detecting symmetries in polynomial Bézier curves
2015, Journal of Computational and Applied MathematicsThe conditions for the coincidence or overlapping of two Bézier curves
2014, Applied Mathematics and ComputationCitation Excerpt :According to Lemma 2, for a prime n a red curve never appears in the nth column. In consequence, no improperly parameterized quadratics (n = 2) or cubics (n = 3) exist, aside from straight lines, as Sederberg [15] already noted. In contrast, there exist improperly parameterized quartics (n = 4), from parameter substitution of degree r = 2 in a quadratic (m = 2).
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This research was performed under a grant from General Electric Company.